Associating reservoir operations with 2D inundation risk and climate uncertainty

Optimizing reservoir operations and schedules is critical for disaster prevention and water resources management. Downstream flood resilience can be maximized by identifying and implementing the optimized reservoir strategies (Serra-Llobet et al. 2022), which requires considering the potential hazard of inundation by floodwaters (Cea & Costabile 2022). The analysis of flood propagation could usually be carried out by the 2D hydrodynamic models, which are useful in forecasting the inundation conditions for residential areas (Bhandari et al. 2018), developing flood risk zones (Farhadi & Najafzadeh 2021; Erima et al. 2022), and assessing the floodplain adaptive measures (Kalra et al. 2020). However, hydrodynamic models are usually intrinsically complex and computationally expensive, so existing reservoir operational optimization often relies on simplified routing methods (Dang et al. 2020; Wei et al. 2022; Ding et al. 2023) or neglects downstream routing (Dahmani & Yebdri 2020; Nourani et al. 2020).

Flood disasters fall within the realm of hydroclimatic calamities, often intricately linked with climate change (Rahman et al. 2021; Munawar et al. 2022). The climate drivers affect the flood risk mostly through the altered peak discharge, while reservoir buildup and operations also have an influence on flood risk (Tang et al. 2021). So, reservoir management needs to be framed in variable future climates (Nourani et al. 2020; Sun et al. 2023), though such studies often mainly focus on inflow availability instead of downstream flood risk.

Given multiple variables to consider for determining the reservoir releases, various algorithms have been developed to optimize the reservoir discharge curve, such as the linear and dynamic programming (DP) (Little 1955), genetic algorithm (GA) (Anand et al. 2018), or neural networks (Zhang et al. 2018). The particle swarm optimization (PSO) algorithm, as an intelligent algorithm that mimics a flock of birds foraging for food, was first proposed by Kennedy & Eberhart (1995) and has become widely accepted as an optimization method in hydrologic models ever since. Kennedy (1997) studied the components and parameters of the PSO algorithm and gave the theoretical significance and reasonable range of each parameter. Clerc (1999) introduced the convergence parameters to improve the convergence speed of the algorithm. Spiliotis et al. (2016) used the PSO algorithm combined with the water supply modeling system to optimize reservoir regulations that effectively reduced the deficits of water supply demands during droughts. Al-Aqeeli & Mahmood Agha (2020) developed a PSO model for individual reservoirs to maximize the annual hydropower generation using the annual reservoir generation as an objective function. Diao et al. (2022) proposed a simulated annealing particle swarm optimization (SAPSO) algorithm to treat the cascading reservoir system with the objective of maximum peak reduction.

When compared to the GA, evolutionary planning, and other algorithms, the PSO algorithm was proved as an effective global optimization method (Parsopoulos & Vrahatis 2002). Mirza et al. (2020) combined DP with the PSO to propose a DP-PSO algorithm, which outperformed the DP-GA algorithm in terms of search space and computational efficiency. Zarei et al. (2019) combined the PSO with the Bat Algorithm to improve the convergence speed of the algorithm by over 20%. Jahandideh-Tehrani et al. (2020) summarized 22 existing algorithms that evolved from PSO algorithms and compared them with evolutionary algorithms and mathematical optimization algorithms, showing that most of the PSO algorithms outperformed GA, mainly in terms of faster convergence. Ma et al. (2021) proposed spark-based parallel dynamic programming and spark-based parallel particle swarm optimization (SPPSO) methods based on cloud computing and found that SPPSO algorithms converged fast and could jump out of the local optima. The PSO has also been applied to optimize reservoir operations for multi-objectives such as water supply, flood storage, and hydroelectric power production and was proved to achieve comparable effects as the non-dominated sorting genetic algorithm II (Afshar & Hajiabadi 2018; Hojjati et al. 2018).

Collectively, the reservoir optimization and downstream inundation prediction were often vaguely considered together but conducted separately, which led to great uncertainty to flood risk management at the watershed scale. If any downstream fluvial flooding is considered, most current practices relied on the 1D channel routing model to predict the hydrograph at the critical cross-section, which hardly predicts the spatial inundation areas and potential consequences, especially to the critical infrastructures at the riparian. Furthermore, current studies rarely associated the climate variations with the reservoir management for the watershed scale, other than their effects on increasing the reservoir storage and overflowing risk (Beiranvand & Rajaee 2023).

Therefore, this work delves into the correlation between reservoir optimization scheduling and downstream inundation while evaluating solutions to the challenges posed by future climate change on reservoir optimization. For this purpose, the reservoir operational model, essentially a hydrologic model, was integrated with the 2D hydrodynamic model accordingly. The effects of the conventional and optimized reservoir operations were compared during four typical historic flood events. The reservoir releases through different operations drove a hydrodynamic model to simulate the effect of reservoir management on the channel safety at critical cross-sections and the downstream inundation risk in different climate scenarios. By comprehensively considering the 2D flood inundation levels at downstream, this work transcends traditional 1D channel model-based scheduling strategies. Through the comparison of two different release plans optimized by the PSO algorithm, this work provides a new finding that points out the necessity of considering the downstream inundation during the optimization of reservoir operations. This finding not only provides water resource managers with a more effective strategy for flood risk control but also aids in enhancing the efficiency of reservoir management to confront the increasingly severe impacts of climate change.

Completed in 2015, the Nierji Reservoir was the largest water conservancy project in the Nenjiang River basin. It is located 189 km upstream of Qiqihar, which is the downstream flood control point that the Nierji reservoir protects. The upper river basin above the reservoir covers 22.35% (66,400 km²) of the entire Nenjiang River basin area, with an annual inflow of 104.7 × 10⁸ m³, accounting for 45.7% of annual runoff in the Nenjiang River basin. As an earth–rockfill reservoir made of asphalt concrete, it was designed for the 1,000-yr flood control standard. The characteristic water levels and the corresponding storage capacity of the Nierji Reservoir were listed (Liang et al. 2021) (Table 1).

The study selected four significant historical events as design floods that occurred in the Nierji-Qiqihar reach: Type 1969 (Gao et al. 2008), Type 1988 (Gao et al. 2007), Type 1998.6 (Liu et al. 2020), and Type 1998.8 (Guan et al. 2021); the first three represent the floods coming from the reservoir point, while the last one incorporates the influence of the lateral inflows from the intermediate basins within the reach (Ding et al. 2023). Type 1998.8 represents a historical extreme case, which caused 14,800 m³/s peak flow and exceeded the safety capacity of the flood control infrastructures at Qiqihar. These pivotal design floods served as benchmarks for assessing the flood simulation tools and reservoir operations before implementation (Lu & Zhang 1999).

The performance of the Nierji Reservoir in terms of flood storage, peak reduction, and postponing the flood arrival has far-reaching implications for the normal functioning of the downstream cities such as Qiqihar with a population of 1,237,300. The suburban levee is 136 km long and is distributed along the city which is designed for a 50-yr event with a peak flow of 8,850 m³/s. The urban levee of Qiqihar is 47 km long, which is designed for a 100-yr event with a peak flow of 12,000 m³/s (Ding et al. 2023).

According to the preliminary design plan to minimize the flood peak at Qiqihar, a conventional operating model was established to represent the current operations that met the downstream flood control standard as follows (Liang et al. 2021):

• (a) During a flood event with a less than 50-yr return period, the peak flow at Qiqihar should be less than 8,850 m³/s.

• (b) During a flood event of the 50–100-yr return period, the peak flow at Qiqihar should be less than 12,000 m³/s.

• (c) The operational water level of the reservoir should not exceed 216 m.

• (d) The maximum water level of the reservoir shall be less than 218.15 m.

The maximum peak reduction downstream at Qiqihar was chosen as the optimization objective. The reservoir discharge was optimized through the PSO algorithm, which should meet the safety requirements of the reservoir and, at the same time, provide storage for the beneficial use of flood water. The water level of the reservoir was updated based on a simple water balance considering the inflow and discharge.

Based on the Type 1969 design flood as an example, the HEC-RAS software was used to simulate the 2D flood inundation in three scenarios (flood, conventional operation, and optimized operation) to analyze the flood control effects of conventional and optimized operations. In the flood scenario, the pre-dam discharge at Qiqihar was estimated by applying the flow time series of the corresponding return periods, e.g. 50 yr, as the boundary condition at the location of the reservoir to drive the 2D inundation simulation as if the dam was unbuilt. This serves as a baseline to evaluate the effects of reservoir operations.

Most of the relevant studies targeted the hydrograph of a downstream river cross-section during reservoir optimization, which failed to take account of the spatial information such as the flood inundation. Due to the stochastic diversity of the optimization method, two PSO-based optimized operations were compared for different flood scenarios. For the PSO₁ plan, the peak flow at Qiqihar tended to be higher and the flood discharge dropped quickly during the receding stage. For the PSO₂ plan, the peak flow at Qiqihar was relatively lower and the flood discharge was maintained at a high level during the receding stage. Both plans met all other necessary constraints. In this way, PSO₂ was characterized by the lower flood peak as the common optimization objective that mainly focused on the hydrograph at the critical downstream cross-section, while PSO₁ was characterized by less flood discharge during the receding stage which led to lower total volume and inundation. So, the influence of the different optimization strategies focusing on the peak reduction and inundation extents could be closely compared.

The global average precipitation was projected, based on the SSP1-2.6 scenario, to increase by approximately 2.9% (1.0–5.2%) in the phase of 2081–2100 compared to the phase of 1995–2014. In the SSP3-7.0 scenario, the global average precipitation was projected to increase by about 4.7% (2.3–8.2%) in the period of 2081–2100 compared to the period of 1995–2014 (Lee et al. 2021). Based on the simulation of the above two climate scenarios, distributed projection data were obtained on the percentage increase in winter and summer precipitation in Northeast China for the period 2081–2100 compared with the period 1995–2014.

To accommodate the phases of 2081–2100 and 1995–2014 in the climate scenarios, the Type 1998.6, 50-yr design flood, falling within the current phase, was used as the baseline. During the flooding season in the summer, the reservoir inflow was predicted to be enhanced by 0–10% in the SSP1-2.6 scenario and by 10–20% in the SSP3-7.0 scenario for the study region. For these two climate scenarios, the inflow was designed to increase by 10% and 20% correspondingly to provide indications to compare the conventional and optimized reservoir operations in the future climate. The flood inundation was simulated for those two climate scenarios, and the inundation risk was analyzed to serve as a reference for developing future flood control measures.

The conventional regulation model, based on the established rules, describes a critical state of flood control, which just meets the downstream safety discharge rate at Qiqihar. The optimization model fully utilizes the reservoir storage and reduces the downstream discharge at Qiqihar (Table 2). Consistently, the optimization of the reservoir operations for the 50-yr design floods was relatively more effective than that for the 100-yr design floods, and the ratio of the peak reduction in the former turned out to be 3–5% higher than the latter.

Therefore, the effect of the optimized reservoir management could be graded differently with and without considering the inundation process. If the single-point peak discharge was used as the optimization objective as a common practice, the PSO₂ optimized operation, which achieved 12.13 m³/s lower peak flow than the PSO₁ operation, should be regarded as a better strategy. However, the comparison of the inundation areas indicates that the PSO₁ operation, achieving the lower inundated area, could be regarded as a better strategy for reducing flood exposure (Table 5). Such conflict indicates the necessity of adding the downstream inundation risk as an additional optimization objective or an evaluation metric, which, however, was neglected by most current studies.

The discrepancy from the current safety standard indicates that the new drainage threshold as well as more rigorous adaptive measures, such as consolidating river embankment, should be proposed for the future climate. This also agrees with the previous finding that reservoir operations cannot completely eliminate the increasing risks of future floods for this region (Sun et al. 2023). Although climatic factors are rarely considered in practical reservoir operations due to their long-term effects and uncertainty, it is found in this study that neither the conventional nor optimized reservoir operations may guarantee a safe release schedule, because the requirement of the maximum allowed flow at the downstream flood control point becomes outdated.

Targeting the current research gap between the reservoir operations and the inundation risk compounded with climate variations, this work integrated a hydrologic reservoir management model with a 2D hydrodynamic model. The scheduling of the reservoir release was controlled by a conventional regulation model and an optimized model based on the PSO algorithm. Through the comparison, it was found that the optimized operation was always better than the conventional operation in terms of effectively managing the peak discharge at the downstream flood control cross-section and controlling the downstream inundation.

Two reservoir operations optimized by the PSO algorithm were developed with the PSO₁ plan focusing on a smaller inundation area and the PSO₂ plan focusing on the peak reduction at the flood control point. The comparison indicates that the PSO₂ plan was more effective when the single-point peak reduction was the only objective as the common practice, while the PSO₁, regarded as the worse choice due to the lower single-point peak reduction, achieved a smaller inundation area that is more favorable for the basin-scale flood resilience. Such conflict indicates the necessity of considering the downstream inundation risk as an additional objective or an evaluation metric during reservoir optimization, which, however, was neglected by most current studies.

This work highlights the need to incorporate 2D downstream inundation risk into reservoir operational optimization frameworks. This imperative becomes particularly urgent, given the projected rise in flood risk due to changing climate patterns. Despite the apparent efficiency of the PSO algorithm in optimizing reservoir operations for the current climate, our analysis proves its inability to address the future climate. Even after the optimization, the downstream area could still expect increased flood exposure due to the increased inundation area and the exceeded safety discharge rate at the flood control cross-section. This indicates that the current maximum allowable flow rate at the flood control point has become outdated and needs to be updated for the future climate.

This work reveals the complex relationship between the reservoir operation and downstream inundation, when dealing with the immense challenges posed by the upcoming climate change. The discrepancy between associating the reservoir operation with and without inundation risk highlights the need to establish the dynamic feedback between the inundation risk and reservoir operations. Jointly addressing this human–natural process could enhance our preparedness for flood risks under future climate conditions.

This work was kindly supported by the Scientific Research Program of The Education Department of Jilin Province (JJKH20231179KJ).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.